K.Z.
Hi Deborah,
It will be fine. I've been traveling with my son since he was four months old (he's now 19 months), and he's earned enough frequent flier miles on two airlines for a free ticket. He's such a pro that he walks down the aisle of the airplane all by himself and knows to take his shoes off at the security line.
Anyway, some easy tips to remember when flying with a little one. Change your daughter's diaper just before you get onto the plane to hopefully avoid changing her on the plane. Some airlines have changing tables in the bathrooms (United and American), while others don't (Southwest and I believe Frontier). In any case, the airline bathrooms are really cramped and it's tough to change a baby in them. Bring some new toys, books, etc. on the plane with you and let her explore them one by one. It was suggested to me by a friend to bring Band-aids (like stickers, but easily removable if they get stuck on the window or tray), dental floss (it's pretty cool to pull and pull and pull the floss out of the holder), and a Magna-doodle (no mess and fun to scribble). Don't forget her lovie or blanket in case she takes a nap on the plane, which is a definite possibility. My son usually zonks right out when we get into the air, even if it is not anywhere close to his naptime. Brings snacks and food for her to eat if she gets hungry, and try to nurse her during takeoff and/or landing to help clear her ears. And definitely bring a change of clothes for her and a clean shirt for you. You never know when she may have a blowout or a spill that would require one or both of you to need a change. I've only had it happen once (my son had a MAJOR blowout that required a full clothing change while we were still in the air), but I was so thankful to have the clothes available.
Most of all, take a deep breath and relax. Babies pick up on mom and dad's anxiety and will get stressed if you are stressed. You'll be fine, and so will your daughter!
Have a great trip!